Learning and doing algebra
Learning and doing algebra (ME322) examines the nature of algebra and how children learn. It develops your awareness of choosing and using symbols and your ability to express general mathematical statements. You’ll meet ideas in the pedagogy (learning and teaching) of algebra, such as the progressions from number to algebra and the importance for learners of expressing and interpreting relationships in words, diagrams and graphs. You’ll learn ways to identify and analyse your own and others’ algebraic reasoning. If you work or plan to work within education, this module is an important step towards achieving your aims.
What you will study
The module comprises eight units:
Unit 1: The nature of algebra
You’ll meet some definitions of school algebra and algebraic thinking. You’ll tackle problems that approach algebra as a way of exploring and expressing generality. And read about moving between well-chosen examples and generalisations and appreciating the role of freedoms and constraints. Additionally, you’ll develop algebraic expressions for simple numerical problems and encounter ideas from research and classroom practice about learning to interpret and treat algebraic symbols.
Unit 2: Representing structural relationships
You’ll tackle problems involving making your algebraic conjectures and convincing yourself when these are true. Taking an approach that algebra is a way of noticing underlying structure, you’ll meet a range of early-algebraic representations used in classrooms, such as bar models and Cuisenaire rods. You’ll read about choosing algebraic representations and work on problems with a learner.
Unit 3: The power of symbolising
This unit focuses on the power of using algebra symbols and the difficulties people experience. You’ll reflect on the choices we make when symbolising and how symbols help create convincing proofs. Additionally, you’ll meet the module idea ‘Manipulate, Get a sense of, Articulate’ that connects learning progression with choice of representations.
Unit 4: Equivalence and the equals sign
You’ll read and tackle problems that help you to notice different ways in which numeric and algebraic expressions can be equivalent, including how learners use the equals sign. You’ll meet two new module ideas: ‘Doing and undoing’ underpins some widely used methods of solving linear equations; ‘Productive lingering’ describes how teachers take time over small steps of algebraic reasoning. You’ll also undertake a project where you adapt a given task and work on it with your learner.
Unit 5: Invariance and change
You’ll focus on algebraic thinking as noticing change and, amidst this change, expressing properties or relationships stay the same. You’ll tackle problems that require you to organise and represent change in one or more variables, particularly sequences problems. Additionally, you’ll create a presentation that identifies invariance and change in your algebraic reasoning.
Unit 6: Covariant relationships
This unit focuses on covariation: how two or more variables change in relation to one another. You’ll tackle problems involving algebraic expressions and graphs. You’ll also learn to use Cornerstone Maths and Geogebra, two digital environments designed for education, to depict covariant relationships and reflect on the affordances of different representations.
Unit 7: Exploring functions and graphs
You’ll focus on functions, including the properties and contexts that give rise to linear, quadratic and exponential functions. Then, having now met all the module ideas, you’ll choose appropriate ones to identify algebraic thinking in your own mathematics and that of your learner. This forms the basis of your end-of-module assessment.
Unit 8: Progressing to geometry
This final unit makes connections between algebra and geometry, supporting progression to Learning and doing geometry (ME321).
You can find the full content list on the Open mathematics and statistics website.
You will learn
You’ll learn to:
- apply ideas from the field of mathematics education for analysing algebraic thinking and learning, specialising in the algebraic content and processes relevant to 11–16-year-olds
- apply a range of approaches to algebraic problems in your own mathematics and in interpreting learners’ algebraic activity
- formulate approaches to teaching
- communicate algebraic thinking, including adapting problems to suit learners
- formulate a personal perspective on issues covered in the module and reflect on developments in your thinking
- use graphing software to support the learning of algebra.
There is no formal pre-requisite study, but we recommend that you study Mathematical thinking in schools (ME620) before or alongside this module.
The ability to write reports in good English is needed for the assignments. You can find support developing academic English in our Help Centre.
The free course Teaching mathematics is good preparation for this module, particularly Weeks 4 and 5.
You’ll have access to a module website, which includes:
- a week-by-week study planner
- course-specific module materials
- audio and video content, filmed in schools
- independent study readings from the OU Library
- free educational software
- assignment details and submission section
- online tutorial access.
We’ll also provide you with three printed algebra task booklets, each covering 2–3 units of study.
You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS (11 'Big Sur' or higher).
Any additional software will be provided or is generally freely available.
To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).
Our module websites comply with web standards, and any modern browser is suitable for most activities.
Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.
It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.